Proving a Negative Claim

Let's put this common refrain to rest~ something that I hear all the time in arguments concerning religion. It goes something like this:

" Remember, you can't prove a negative!"

Really people?

This has become much more common, especially in the arguments amongst Atheists and agnostics concerning certainty, and it really puzzles me how people can be skeptical and free-thinkers, yet take to an idea so easily and not question it. I will elaborate on this a little more once I have the time, but let me start all of those "can't prove a negative" types off with a question~ " I am not sitting at my desk." Thats a negative claim. Are you telling me that there is no way to confirm or disprove that?

The point is simply that -in anything except trivial cases- proving a negative is practically impossible. That is the crux of the issue. Sure, you can prove trivialities like "There is no elephant in my room" or "There is no cat in my trunk".
But just stretching the claim to propositions that are slightly less trivial, like "There is no black widow spider hiding somewhere in my house" makes it immediately clear that the workload is starting to increase exponentially. In order to prove that claim I'd have to have a whole team of people searching through my house in sections (so the alleged spider can't move through the sections) for possibly several days.
Increasing the claim again, once we get to "There is no purple black widow with yellow spickles hidden somewhere in Belgium" and we are already far beyond what can be practically proven. The same is true for flying reindeer somewhere on the North Pole, Atlantis somewhere on the bottom of the sea, fairies living in some unexplored part of our forests, God living in some unspecified realm 'outside' the universe, etcetera...

All of these are -while perhaps theoretically provable in a theoretical sense- just impossible to prove in any practical sense. That's why we say that proving negatives cannot be done.

But moreover and more importantly, it's not anyone's responsibility to be able to disprove a negative.

What do you need to prove something? I say the only thing that can prove something is evidence that has been put through the scientific method. Evidence itself cannot provide proof for everything that exists or happens. A magician will offer "magic" as evidence that the impossible is true, but our reason tricks us, so we need the scientific method as a tool to augment our reason. So, proof is evidence, but lack of evidence does not mean there is not evidence yet to be found. Lack of evidence is not proof of a negative!!!!!

"Well, that may be a question of trying to prove a negative, but the inverse of that question is just as hard to prove as the original version. You have simply discovered a set of questions that are hard to answer. It has nothing to do with the questions being "proof of a negative"."

Fair point.

The nuance I would make there is that you assume both claims are made in a vacuum, i.e. you're assuming that I would make the claim that "There is a black widow spider in my house" for no reason at all, and that I would then have to go out and find the evidence.

One of the reasons proving a negative is so hard (assuming that you're right) is that there's never a point you can stop and see that you're right; you have to follow the rigorous proof through all the way.

For instance, if I go out to prove that Atlantis once existed, all I really have to do is find my first piece of good evidence and then I'm done. Now, even if I'm right, that might still be a difficult quest; but that's not the point: the point is that if I am in fact right, then I will be able to eventually find some evidence and I'll be able to stop right there.

However, if I want to go out to prove that Atlantis never existed, the quest never stops until I have in fact explored every square metre of the world's oceans. Logically speaking, my proof is not rigorous until I have walked through the entire set.

So I can't say that I fully agree. The workload required to prove negatives is still volumes more than the reverse. I think that's also what happens in our daily lives: we're faced with claims that, if they were really true, proponents should have little difficulty providing some evidence to show that there's a there there; yet, because they are not in fact true, they are still a pain in the ass to actually disprove.

But yes, Park, you're correct to say that it is theoretically possible. It just isn't usually practically feasible.

I think your point is indeed valuable to keep in mind. In a way it's an extension of the falsification principle which says a proposed thesis must be phrased and formulated in such a way that it yields testable criteria; which we can use to see if the thesis passes or fails our tests. And that of course means the claim can't be too vague, it needs to have manifestations in reality, etcetera etcetera.

But even with all that said and done, I think it's still valuable to point out that proving a negative is harder, just because you are required to run over the entire set of possibilities for your proof to be rigorous.

Even if I make a rather clear-cut definition for Atlantis (like that it lies somewhere between Ireland and Iceland at the bottom of sea), it's still easier to prove the positive than the negative. Proving the positive (if it's in fact the correct answer) could happen relatively rapidly (theoretically you could get lucky on your first dive for it), whereas proving a negative (if it is the correct answer) will always require a full search and a full exploration of every location, and never anything less (because you can't get lucky).

The line between having evidence of existence and reasoning your way to a definition is not always a clear one.

Do we have evidence of the existence of dark matter yet, or are we simply reasoning our way to a definition? Considering it is still largely a term rather than a concept, it seems the latter.

What about the Higgs Boson? At what point do you draw the line of "having enough evidence to think it's worth looking for" and "reasoning your way to the definition" (using mathematics). It's simply a continuum.

The same goes for the monster of Loch Ness, Bigfoot or any other fantastical creature. Some will say that (probably fake) personal testimonies and (probably fake) artifacts are enough to have some "evidence of existence", others will still say that they're making up a definition.

How do you draw the line? As with many instances of pseudo-science, there's no simple answer to that question.

The scientific method is a tool that has served very very well as a bullshit finder. Dark Matter is a term given to evidence that we do not understand yet and the Higgs Boson is something that is an idea that is being predicted by scientists based on prior evidences gathered and understood.

There is no God, therefore one can't prove a negative, But there is a vast convergence of evidence from all of the sciences, especially psychology, that support the fact that the God concept is the product of the human mind. There are no absolutes in science, so an Atheist doesn't have to prove there is no God. Simply put, based on the accumulated knowledge throughout human history and our understanding of human nature, and human psychopathology it is far more likely that there is no such thing as God. Or as Richard Dawkins put it in his book, The God Delusion in chapter 4 - Why there almost certainly is no God.

There are no free luches. Or the odds of probability of an uncaused God is impossible.